6(3x-2)-(3x-2)(3x-2)=0

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Solution for 6(3x-2)-(3x-2)(3x-2)=0 equation: 


Simplifying
6(3x + -2) + -1(3x + -2)(3x + -2) = 0

Reorder the terms:
6(-2 + 3x) + -1(3x + -2)(3x + -2) = 0
(-2 * 6 + 3x * 6) + -1(3x + -2)(3x + -2) = 0
(-12 + 18x) + -1(3x + -2)(3x + -2) = 0

Reorder the terms:
-12 + 18x + -1(-2 + 3x)(3x + -2) = 0

Reorder the terms:
-12 + 18x + -1(-2 + 3x)(-2 + 3x) = 0

Multiply (-2 + 3x) * (-2 + 3x)
-12 + 18x + -1(-2(-2 + 3x) + 3x * (-2 + 3x)) = 0
-12 + 18x + -1((-2 * -2 + 3x * -2) + 3x * (-2 + 3x)) = 0
-12 + 18x + -1((4 + -6x) + 3x * (-2 + 3x)) = 0
-12 + 18x + -1(4 + -6x + (-2 * 3x + 3x * 3x)) = 0
-12 + 18x + -1(4 + -6x + (-6x + 9x2)) = 0

Combine like terms: -6x + -6x = -12x
-12 + 18x + -1(4 + -12x + 9x2) = 0
-12 + 18x + (4 * -1 + -12x * -1 + 9x2 * -1) = 0
-12 + 18x + (-4 + 12x + -9x2) = 0

Reorder the terms:
-12 + -4 + 18x + 12x + -9x2 = 0

Combine like terms: -12 + -4 = -16
-16 + 18x + 12x + -9x2 = 0

Combine like terms: 18x + 12x = 30x
-16 + 30x + -9x2 = 0

Solving
-16 + 30x + -9x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-8 + 3x)(2 + -3x) = 0


Subproblem 1
Set the factor '(-8 + 3x)' equal to zero and attempt to solve:

Simplifying
-8 + 3x = 0

Solving
-8 + 3x = 0

Move all terms containing x to the left, all other terms to the right.

Add '8' to each side of the equation.
-8 + 8 + 3x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + 3x = 0 + 8
3x = 0 + 8

Combine like terms: 0 + 8 = 8
3x = 8

Divide each side by '3'.
x = 2.666666667

Simplifying
x = 2.666666667

Subproblem 2
Set the factor '(2 + -3x)' equal to zero and attempt to solve:

Simplifying
2 + -3x = 0

Solving
2 + -3x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + -3x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3x = 0 + -2
-3x = 0 + -2

Combine like terms: 0 + -2 = -2
-3x = -2

Divide each side by '-3'.
x = 0.6666666667

Simplifying
x = 0.6666666667
Solution
x = {2.666666667, 0.6666666667}

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